a = 5.2 cm and B = 67°.
Work out the area of the triangle. Round
your answer to 1 DP.

From the given quadratic function ff(x) = (x² + cx - 1)/(2x² - 3x + 2), we can tell that the possible values for which the function  lies on the interval (-1, 2) is; c c ≤ 12

We are given the quadratic function f(x) as;

f(x) = (x² + cx - 1)/(2x² - 3x + 2)

Now, we want to find the possible values of c for which the function belongs to the interval (-1, 2). Thus, we will plug in -1 for x and equate the function to 2;

f(-1) = ((-1)² + c(-1) - 1)/(2(-1)² - 3(-1) + 2) = 2

(1 - c - 1)/6 = 2

-c/6 = 2

c = -12

Thus, the possible values  for which the given function f(x) belongs to the interval (-1, 2) are; c ≤ 12

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M is not like the others. ratio and proportion is used.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8 (or 3:4). (or 4:7). Any number of quantities, such as counts of people or objects or measurements of length, weight, or time, etc., can be included in a ratio. In most cases, both numbers must be positive.

Shorter diameter of L is 3:4.
the ratio of M is 4/8= 1:2
the ratio of N is 9/12= 3:4 (count the squares)
so, M is not like the others.

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The times that the ball is 34 feet high to the nearest tenth of a second is equal to 4.61 and 0.39 seconds.

In order to determine the time or times for this ball at a height of 34 feet, we would simply substitute the value of the height into the function h(t) as follows;

h(t) = -16t² + 80t + 5

34 = -16t² + 80t + 5

Re-arranging the equation, we have:

16t² - 80t + 34 - 5 = 0

16t² - 80t + 29 = 0

Next, we would solve the quadratic equation by using the quadratic formula:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-80)\; \pm \;\sqrt{-80^2 - 4(16)(29)}}{2(16)}\\\\x = \frac{80\; \pm \;\sqrt{6400 - 1856}}{32}\\\\x = \frac{80\; \pm \;\sqrt{4544}}{32}[/tex]

x = (80 ± 8√71)/32

x = (80 + 8√71)/32  and  x = (80 - 8√71)/32

x = 4.61 and 0.39 seconds.

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Each relationship should be matched with the correct description as follows:

Direct variation can be defined as a type of proportional relationship in which a variable is directly proportional to another variable.

An indirect variation can be defined as a type of proportional relationship in which a variable is inversely proportional to another variable. This ultimately implies that, an indirect variation represents two variables that are inversely proportional to each other.

In conclusion, a joint variation describes a situation in which a variable depends on two other variables which share a directly proportional relationship.

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22 5/8÷2 2/3 will tell us the number of bows that is there will be some ribbon left over once we have enough to make 8 full bows but not a ninth.

Given that,

To construct one bow, Kim uses 2 2/3 yards of ribbon from a roll.

22 5/8 yards of ribbon can be used to create bows.

We have to find 22 5/8÷2 2/3 will tell us the number of bows.

Take the mixed fractions,

A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls between any two whole numbers.

=22 5/8÷2 2/3

=181/8÷8/3

Change to improper fractions

=181/8×3/8

Multiply by the reciprocal. Nothing cancels.

=543/64

Change into a mixed number

=8  31/64

Therefore, There will be some ribbon left over once we have enough to make 8 full bows but not a ninth.

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Answer:

No

Step-by-step explanation:

Not because the sum of the measurements of the smaller sides (6, 6) must not be equal to or greater than the measure of the larger side (12) since in these conditions the triangle does not exist.

Hope this helps

Using the numbers 12, 6, 6, the triangle can not be formed.

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Here, we have,

given that,

The given numbers are 12, 6 and 6.

Here, 6 + 6 = 12 but not greater than 12

so, we get,

Therefore, using the numbers 12, 6, 6, the triangle can not be formed.

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55cm is 13.75% of 4 meters.

Answer: 12.5%

Step-by-step explanation:

There are 100 CM in 1 M.

4×100=400

50/400=12.5

Every time a construction company submits a bid, the odds of winning are 0.10 percent. With the aid of a binomial distribution, it is possible to calculate the likelihood of selecting a specific number of projects out of 12 bids: TRUE

As it is given in the description itself that the probability of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

Therefore, the statement "every time a construction company submits a bid, the odds of winning are 0.10 percent. With the aid of a binomial distribution, it is possible to calculate the likelihood of selecting a specific number of projects out of 12 bids" is TRUE.

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The complete question is given below:
A construction company has found it has a probability of 0.10 of winning each time it bids on a project. the probability of winning a given number of projects out of 12 bids could be determined with a binomial distribution. TRUE or FALSE.

Answer:

m = 1

Step-by-step explanation:

A number is divisible by 3 if the sum of the digits is a multiple of 3

the given number is 2m234 and we are asked to find the smallest m

Adding up known digits gives 2 + 2 + 3 + 4 = 11

The next multiple of 3 is 12

So 11 + m = 12

m = 1

The other possibilities are
m = 4, m = 7

10x - 26 = 3x + 23

x = 7

To find out x

10x - 3x = 23 + 26

7x = 49

x = 7

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Answer: x=7

Step-by-step explanation

[tex]10x-26=3x+23\\[/tex]

First you want to get the x's to one side you would subtract 3x from both sides.

Then your equation should be:

[tex]7x-26=23[/tex]

Then you want to add 26 to both sides.

[tex]7x=49[/tex]

Then you would divide both sides by 7, making your answer:

[tex]x=7[/tex]

Total income for Minimum salary: $160 and Commission: 53% on $2900 will be  $1,697.

A salary is a set earnings that an employee normally gets on a weekly, biweekly or month-to-month foundation. A Commission is greater earnings an worker earns once they promote items or services.

We had given the minimum salary of $160 which will be fixed and not depend on the earning of the commission.

Now As given the sale of $2900 and the commission percentage of 53%

∴ Total Commission will be = [tex] \frac{2900\ (53)}{100} [/tex]

∴ Total Commission = 29 (53).

∴ Total Commission = $ 1,537

∴ Total Income will be the addition of base/minimum salary and the commission in total.

∴ Total income will be $160 + $1,537

∴ Total income = $1,697.

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The equation of a line that is perpendicular to y = 3x + 3 is option A y equals negative one-third times x plus 1(-1/3x + 1)

Given,

The equation of line, y = 3x + 3

The line passes through (-6, 3)

We have to find the equation of the line that is perpendicular to y = 3x + 3

Slope of the line, m = 3

Here, in perpendicular case, slope is negative of its reciprocal.

That is, m = -1/3

Now, we can find the equation

y - y₁ = m(x - x₁)

Here,

y₁ = 3

x₁ = -6

m = -1/3

So,

y - 3 = -1/3(x - (-6))

y - 3 = -1/3(x + 6)

y - 3 = -1/3x + -1/3(6)

y - 3 = -1/3x - 6/3

y - 3 = -1/3x - 2

y = -1/3x - 2 + 3

y = -1/3x + 1

That is, the equation of a line that is perpendicular to y = 3x + 3 is y equals negative one-third times x plus 1(y = -1/3x + 1)

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Answer:A is the answer

Step-by-step explanation:

i got it right on the test

Given,

Population Standard deviation = 3.2 inches

Required confidence interval (C) =  95%

Margin of error = 0.55

Let h be the number of randomly selected players surveyed.

∝ = 1 - C = 1 - 0.95 = 0.05

∝/2 = 1 - C / 2 = 0.05/2 = 0.025

Score of ∝/2 = 2.5 - 0.025 = 2.475

We know,

Margin  of error = 0.55

Standard deviation = 3.2

∵ 0.55 = 2.475 x 3.2/ √h

√h = √0.144/1000

∴ h = 12

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Given the Graph functions above, the option that applies in the above scenario are:

A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f might similarly be defined as the graph of the equation y = f. (x). As a result, the graph of a function is a subset of the graph of an equation.

Explanation for Option A:

Note that both functions intersect at some point. That one is where f(g(x)) = g(f(x)) for at least one value of x. Note, this is for the value of x and not y;

Explanation for Option C:

This simply means that on the if f(g) where y = 5,x is 0; for g(f) where y = 5, x = -2.5. This is also observable in the graph

Explanation for Option D

If two functions f and g have the same domain and codomain, and f(a)=g for every an in the domain, we say they are equal (a).

Explanation for Option E
If a graph is cummulative, there will be a noticeable trend either as an upward trajectory or a negative one with the line crossing the origin. This is not the case here.

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Answer:

The expert answer is correct.  But here is the short answer.

1, 3, 4, 5.

Answer:

n = 29/12 is the simplest form

Step-by-step explanation:

145 ÷ 60 = 29/12

Answer:

Step-by-step explanation:

Use the distance formula.

Distance:

[tex]\Rightarrow \sf{\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}}[/tex]

y₂=(-7)

y₁=(-3)

x₂=4

x₁=8

[tex]\sf{\sqrt{\left(4-8\right)^2+\left(-7-\left(-3\right)\right)^2}}[/tex]

Solve.

Use the order of operations.

PEMDAS stands for:

Do parentheses first.

(4-8)=-4

[tex]\sf{\left(-4\right)^2+\left(-7-\left(-3\right)\right)^2}[/tex]

-7-(-3)=-7+3

-7+3=-4

[tex]\sf{\left(-4\right)^2+\left(-4\right)^2}[/tex]

Do exponents.

[tex]\sf{(-4)^2=4^2=4*4=16}[/tex]

Then, you add.

16+16

[tex]\Rightarrow \boxed{\sf{32}}[/tex]

Therefore, the correct answer is C. 32.

Answer:

Try 20.

Step-by-step explanation:

To round 19.5 to the nearest whole number consider the tenths’ value of 19.5, which is 5 and equal or more than 5. Therefore, we have to round up: the whole number part of 19.5, 19, increases by 1 to 20, and the decimal point and all digits (.5) are removed.

19.5 rounded to the nearest whole number = 20

The fruit drink which contains 70 % fruit juice will have 120 pints of 65 % pure fruit juice and 20 pints of 100% pure fruit juice.

Given that:-

Two types of juice are 65 % fruit juice and 100 % pure fruit juice.

The company is attempting to produce a fruit drink that contains 70% pure fruit juice.

We have to find the amount of each of 65% pure fruit juice and 100 % pure fruit juice which contains 70 % fruit juice with 140 pints of total juice.

Let the amount of 65 % pure fruit juice be x pints and,

The amount of 100 % pure fruit juice be y pints

We know that,

x + y = 140 ...(1)

Also,

Using weighted mean, we can write,

(65x + 100y)/(x + y) = 70

65x + 100y = 70x + 70y

5x = 30y

x = 6y

Putting x = 6y in (1), we get

6y + y = 140

7y = 140

y =140/7

y = 20 pints

x = 6y = 6*20 = 120 pints

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The total number of voters is 1200, and out of that 720 voters cast their votes.

Let's take total voters = V

The percentage of voters do not cast their votes due to various reasons is 40%.

Therefore, Voters did not cast their votes = (40÷100)V = 0.4V

As 0.4V voters did not cast their votes. To calculate the total number of voters who cast votes, divide (total) by (non-casted-voters):

Voters casted their votes = V  - 0.4V = 0.6V

0.6V = 720

=> V = 1200

The total number of voters is 1200 if 720 voters cast their votes.

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For the exponential function f(x) = 3(0.5)^x, we have that:

An exponential function is modeled according to the rule given below:

[tex]y = ab^x[/tex]

In which the parameters are described as follows:

For this problem, the rule of the exponential function is given by:

y = 3(0.5)^x.

Hence the parameters are:

a = 3, b = 0.5.

Then:

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Answer:

decay; (0,3)

Step-by-step explanation:

The mean of the sampling distribution of proportion is 0.15

The probability the sample proportion will be within 0.04 of the population proportion is 0.9182

The probability the sample proportion that will be within 0.02 of the population proportion is 0.6157

P(Smokers) in Australia= 15/100=0.15

Sample, n =240

Part a, The mean of the sampling distribution of proportion:

μ₂ = P(Smokers)

    = 0.15

The mean of the sampling distribution of proportion is 0.15

The standard deviation of the sampling distribution of proportion is,

δ [tex]=\sqrt{p\frac{(1-p)}{n} }[/tex]

  [tex]=\sqrt{0.15\frac{(1-0.15)}{240} }[/tex]

 [tex]=0.0230[/tex]

The standard deviation of the sampling distribution of proportion is 0.0230

Part b, The probability the sample proportion will be within +/-0.04 of the population proportion:

To find this, we first, compute the z score then find probability based on standard normal table.

For 0.15-0.04,  p=0.11 and converts to:

   [tex]z=\frac{p-u_{p} }{standard deviation} \\[/tex]

   [tex]=\frac{0.11-0.15}{0.0230}[/tex]

  = -1.74

For 0.15+0.04, p=0.19, and converts to:

    [tex]z=\frac{0.19-0.15}{0.0230}[/tex]

     = 1.74

From the standard normal distribution table, the associated probability for z values and subtracts the probability is,

     [tex]=p(-1.74\leq z\leq 1.74)[/tex]

     [tex]=0.9591-0.0409[/tex]

    [tex]=0.9182[/tex]  

Hence, the probability the sample proportion will be within 0.04 of the population proportion is 0.9182

Part c, the probability the sample proportion will be within 0.02 of the population proportion:

First, compute the z score then find probability based on standard normal table.

For 0.15-0.02, p=0.13, and converts to:

       [tex]=\frac{0.13-0.15}{0.0230}[/tex]

       =-0.87

For 0.15+0.02, p=0.17, this converts to:

    [tex]=\frac{0.17-0.15}{0.0230}[/tex]

    =0.87

From the standard normal distribution table, the associated probability for z values and subtracts the probability is,

    [tex]=p(-0.87\leq z\leq 0.87)[/tex]

   [tex]=0.8079-0.1922[/tex]

   [tex]=0.6187[/tex]

Hence, the probability the sample proportion will be within 0.02 of the population proportion is 0.6157

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The depth of water after 10 minutes is 20 inches which is the option A.

Given that:-

Depth of water in a tank after t minutes is modeled by the function f(t) = 5+1.5t, measured in inches.

Let us check for Option A.

Putting t = 10 min in the given equation, we get,

f(10) = 5 + 1.5*10 = 5 + 15 = 20 inches.

Hence, option A is the right answer.

We can also check the other options to confirm our answer.

Putting t = 20 minutes,

f(20) = 5 + 1.5*20 = 5 + 30 = 35 inches

As 10 inches is written in B, hence, it is not the right answer.

We already know that t = 10 gives 20 inches.

Hence, C is not the answer.

Putting t = 65 minutes,

f(20) = 5 + 1.5*65 = 5 + 97.5 = 102.5 inches

As 10 inches is written in D, hence, it is not the right answer.

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Answer:

[tex]f(x)=3x^4+51x^2+48[/tex]

Step-by-step explanation:

As n = 4, the degree of the polynomial is 4.

Therefore, the function cannot have more than 4 distinct roots.

[tex]\implies f(x)=a(x-p)(x-q)(x-r)(x-s)[/tex]

If a complex number z is a root of f(z) = 0 then its complex conjugate is also a root.  Therefore:

[tex]\implies f(x)=a(x-i)(x+i)(x-4i)(x+4i)[/tex]

[tex]\implies f(x)=a(x^2-i^2)(x^2-16i^2)[/tex]

[tex]\implies f(x)=a(x^2-(-1))(x^2-16(-1))[/tex]

[tex]\implies f(x)=a(x^2+1)(x^2+16)[/tex]

Given f(-1) = 102, then:

[tex]\begin{aligned}\implies f(-1)=a((-1)^2+1)((-1)^2+16)&=102\\a(1+1)(1+16)&=102\\a(2)(17)&=102\\34a&=102\\a&=3\end{aligned}[/tex]

Therefore:

[tex]\implies f(x)=3(x^2+1)(x^2+16)[/tex]

[tex]\implies f(x)=3(x^4+17x^2+16)[/tex]

[tex]\implies f(x)=3x^4+51x^2+48[/tex]

Answer:

The length is 6 ft

Step-by-step explanation:

The area of a square is given by

A = s^2 where s is the side length

36 = s^2

Take the square root of each side

sqrt(36) = sqrt(s^2)

6 =s

The length is 6 ft

Answer:

6 ft

Step-by-step explanation:

We know that the formula to find the area of a square is :

Area = a² ( length × width)

According to the question they've already given the area of the square as 36ft².

So, to find the the measure of a one side, let the in unknown measure of a side be a.

And now, using the formula let us find the value of a ( length of a one side).

[tex] \sf \: Area = a² \\ \sf 36 = a² \\ \sf \: \sqrt{36} = a \\ \sf6ft = a[/tex]

‌

Using percentage we can calculate that 81 students did not take French.

In mathematics, a number or ratio that is expressed as a fraction of 100 is referred to as a percentage. Although the abbreviations "pct" and "pc" are also often used, the percent symbol "%" is the one that is most frequently used. A % is a number that has neither established units of measurement nor dimensions.

The percentage can be calculated by taking the value and dividing it by the total value, then multiplying the result by 100. using the formula (Value/Total Value) × 100% to calculate percentages.

Let the total number of students be x.

Now 91% of this students is equal to 819.

Now using the properties of percentages we can write:

91% of x = 819

or, x = 900

Number of students who did not take French = 900 - 819 = 81

Hence using percentages we can say that 9% or 81 students did not take French.

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Mean time = 142 minutes

One of the the most common expression for the mean of a statistical distribution with random variables is the average of all the terms. The mean of  any given data can be found out by adding all numbers in the data set and then dividing that by the number of values.

First calculate the mid point of the time interval :

(15+17)/2=16

(17+19)/2 = 18

(19+21)/2= 20

(21+23)/2= 22

Multiply each time mid point with respective frequency :

16*5=80

18*12= 216

20*7= 140

22*6= 132

Adding this and dividing by the total number of times that is 4:

= (80+216+140+132)/4

= 568/4

Mean time =142 minutes

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The given distribution is (A) Bimodal skewed as the distribution has 2 humps.

As the given graph has 2 humps, we can conclude that the given distribution is an (A) Bimodal skewed.

Therefore, the given distribution is (A) Bimodal skewed as the distribution has 2 humps.

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About 200 teddy bears in the store.

Given,

The ratio of the number of dolls to the number of teddy bears is 6:5

and,  The store has 240 dolls.

To find the number of teddy bears are in the store.

Now, According to the question:

Total no. of dolls are 240

The ratio of dolls and teddy bears are 6:5

Then, For dolls

= 240/6 = 40dolls

So, Teddy Bears = 40 × 5 = 200

Hence, About 200 teddy bears in the store.

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